Primel Time Units
Fundamental Reality: The Mean Solar Day The mean solar day is a fundamental reality of human life. Accordingly, Primel uses a simple dozenal power of the day, the hexciaday (z|10-6 days) as its base unit of time, the ′timel. This comes out to d|50/1728 or d|1/34.56 of a second (z|0.042 s, or d|0.02893518 s), making this quite a fleeting moment of time, a bit shorter than the frame period for typical movie film, and hence just beyond human perception. This happens to be very close to the vibration period for a C♯0 musical note. For this reason, dozenalists in the past have called this a "vic" (short for "vi-bration of C"). However, perhaps we can do better than this, and find an existing English word that captures the sense of brevity of this unit: Primel proposes to nickname this the ′jiffy. Although the ′jiffy is a very short an interval indeed, it is nevertheless a useful quantity for precision scientific and engineering purposes. Not to mention sports, especially the Olympic variety, where a down-to-the-′jiffy time might mean the difference between a medal made of bronze or silver, and one of gold! In any event, given the principle of 1:1 correspondence of base units Primel adheres to, this sizing for the ′timel will have interesting effects on the rest of the units in the metrology. On the other hand, the unqual powers of the ′timel do fall within the range of human perception, starting with the ′unquatimel (z|101 ′timels). This is equivalent to the pentciaday (z|10-5 days), which comes out to d|50/144 of a second (z|0.42 s, or d|0.3472 s). In the past, dozenalists have dubbed this unit the "dovic" (short for "a dozen vics"). But perhaps we can we find a nickname that is a little more evocative. Note that this unit is at a little over a third of a second, and therefore about the time it takes to blink an eye. Accordingly, Primel proposes to colloquialize this unit as the ′twinkling. So a dozen ′jiffies make a ′twinkling. The ′biquatimel (z|102 ′'''timels) is equivalent to the '''quadciaday (z|10-4 days). This comes out to d|50/12 of a second (z|4.2 s, or d|4.16 s). This counts out a dozen ′twinklings in slightly over four seconds. If these were beats of music, then it would correspond to 4 measures of 3/4 musical time at d|172.8 beats per minute, an Allegro Vivace tempo. This is enough, for example, to express the melodic theme of a typical Viennese waltz (such as Strauss' Blue Danube). Hence, Primel proposes to nickname this interval a ′waltzing. The ′triquatimel (z|103 ′timels) is equivalent to the triciaday (z|10-3 days). This comes out to exactly d|50 seconds (z|42 s), which makes it a minute-like quantity, although a bit shorter. For that reason, dozenalists in the past have suggested naming this a "minette". However, perhaps we could find a name that is less beholden to sexagesimal and more appropriate for a dozenal measure. Notice that the digit root tri appears in both the triqua prefix in ′triquatimel and the tricia prefix in triciaday. The English word "trice" is a poetic and somewhat archaic word signifying a short period of time; although its etymology is not actually cognate with "three", it is punningly suggestive of that meaning. Consequently, Primel proposes to nickname this unit the ′trice. So a ′trice consists of a dozen ′waltzings. It is exactly intermediate on the logarithmic scale between the day and the ′timel: a day consists of z|1000 (d|1728) ′trice, and a ′trice consists of z|1000 (d|1728) ′jiffies. The ′quadquatimel (z|104 ′timels) is equivalent to the biciaday (z|10-2 days). This comes out to exactly d|600 seconds (z|420 s), or ten minutes. This is equivalent to a dozen ′trice. It's interesting to note that, the decimal figure for "d|10 minutes" resembles the equivalent dozenal figure for "z|10 ′trice". (Twenty (d|20) minutes is equivalent to two dozen (z|20) ′trice, thirty (d|30) minutes is equivalent to three dozen (z|30) ′trice, and so forth.) In the past, dozenalists have suggested naming this time unit the "temin", as a corruption of "ten minutes". However, deriving a name for a dozenal unit from a decimal word ("ten") and from a unit ("minute") not appearing as part of a dozenal metrology, does not seem very apt. The same argument can be leveled against a more conventional construction such as "decaminute". Instead, Primel proposes giving this unit the nickname ′bout, which is suggestive both of a unit of time and of the "bout" of action needed to take a clock hand that rotates once per ′trice, and spin it a dozen times. The ′pentquatimel (z|105 ′timels) is equivalent to the unciaday (z|10-1 days), a dozenth of a day. This comes out to exactly d|120 minutes (z|Ӿ0 min), or two hours. In the past, dozenalists have suggested naming this time unit the "duor", as a corruption of "double hour". However, this would be just as derivative as "temin". The same argument could be leveled against a more conventional construct such as "bi-hour". A nickname for this unit that could stand on its own would be preferable. Primel proposes colloquializing this unit as the ′stound. This resurrects an archaic Old English word that at one time meant "time of day", but which was supplanted after the Norman Conquest of d|1066 (z|74Ӿ) C.E. by the word "hour" borrowed from the French. Hence, a day consists of a dozen ′stounds, and a ′stound consists of a dozen ′bouts, or z|100 ′trice. The ′hexquatimel (z|106 ′timels) is, of course, the mean solar day. Making the day a simple dozenal power of the ′timel provides certain benefits for applications, such as astronomy, that need to relate larger amounts of time, expressed in days, to smaller amounts of time expressed in, say, ′trice or ′jiffies. As long as dozenal quantities and Primel units are used, all that is needed is to make the proper shift of radix points. There are no extraneous factors to multiply or divide by. Relation of Primel and TGM Time Units Although TGM also considers the mean solar day a "fundamental reality", its base unit of time, the Tim, is actually a simple power of the half day, or "semiday", rather than the whole day. In fact, it is equivalent to the pentciasemiday, or z|10-5 half-days. In Primel terms, the Tim is equivalent to 6 ′timels, and the ′timel is equivalent to 2 unciaTim. Although the TGM time units are not whole dozenal powers of the ′timel, each is a simple multiple of one, so we could incorporate them into Primel as auxiliary units: Additional Auxiliary Primel Time Units Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel. Dozenal Perennial Calendar: Symmetry 454 A Perennial Calendar can be constructed where every year and month starts on the same day of the week and consists of a whole number of weeks, and where a leap year adds a leap week onto the end of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z|24 or z|2Ɛ days and how each year is either z|264 or z|26Ɛ days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z|44 or z|45 weeks. (This is essentially a dozenalization of Irv Bromberg's Symmetry 454 Calendar.) The following calendar is completely in dozenal base. Dozenal Perennial Calendar: Symmetry 676 A variation of the Perennial Calendar would give months either z|26 or z|27 days, but would make each quarter and year a whole number of weeks, with a leap week added periodically at the end of the year. (This is essentially a dozenalization of Irv Bromberg's Symmatry 010 Calendar.) Dozenal Orders of Magnitude: Time This is a Primel version of the